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TZID:Asia/Tokyo
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DTSTART:19510909T010000
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BEGIN:VEVENT
UID:calendar.22535.field_date.0@groups.oist.jp
DTSTAMP:20191122T204223Z
CREATED:20190218T163912Z
DESCRIPTION:Date \n\n \n\n Monday\, February 25\, 2019 - 16:00 to 17:0
0 \n \n Description \n\n \n\n \nAbstract: The sphere packing pro
blem in d dimensions asks for the densest packing of spheres in d-dimensio
nal Euclidean space R^d. Prior to 2016\, the problem had only been solved
in dimensions 2 and 3 (with the solution in dimension 3 being Hales's famo
usly complicated solution to Kepler's conjecture)\, and solutions in most
other dimensions were thought to be out of reach\, except for dimensions 8
and 24 where overwhelming numerical and theoretical evidence supported th
e conjectures pointing at specific lattices as the optimal packings. In a
breakthrough in 2016\, Maryna Viazovska published a stunning proof for the
8-dimensional case\, followed up shortly with a proof for the 24-dimensio
nal case with several coauthors. The solutions work by using a previous re
duction of the problem (due to Henry Cohn and Noam Elkies) to a problem in
harmonic analysis\, and ingeniously solving that analysis problem using n
umber-theoretic tools - specifically\, the mathematics of modular forms.\n
\n\n \n\n\nIn this talk I will give a quick survey of these developments a
nd the beautiful new challenges and opportunities that they open up for at
tacking this classical geometry problem. I will also discuss my own recent
results on infinite series representations for the Riemann xi function an
d explain how Viazovska's work\, which appears not strongly related to the
problem I was studying\, nonetheless provided me with useful inspiration.
DTSTART;TZID=Asia/Tokyo:20190225T160000
DTEND;TZID=Asia/Tokyo:20190225T170000
LAST-MODIFIED:20190218T163912Z
SUMMARY:[Geometry\, Topology and Dynamics Seminar] Viazovska's work on the
sphere packing problem and some recent developments in number theory by Dr
. Dan Romik (UC Davis)
URL;TYPE=URI:https://groups.oist.jp/manifolds/event/geometry-topology-and-d
ynamics-seminar-viazovskas-work-sphere-packing-problem-and
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